In his article “Why Proof? What is a Proof?” (2008) Carlo Cellucci focuses on so-called natural mathematics and natural logic, centering on mathematics and logic embodied in organisms as a result of natural selection, and stressing the different role of “artificial mathematics and logic”, that is, mathematics and logic as disciplines. I will provide further insight into this interplay. The first issue is related to the importance of increasing logical knowledge of abduction: Cellucci himself clearly shows how the study of abduction helps us to extend and modernize the classical and received idea of logic, understood merely as a corpus of axiomatic systems. The second refers to some ideas deriving from so-called distributed cognition and concerns the role of logical models as forms of cognitive externalizations of preexistent informal human reasoning performances. In this perspective, natural mathematics and logic are seen as constitutively intertwined with their “artificial” counterparts. Logical externalization in objective formal systems, communicable and sharable, is able to grant stable perspectives endowed with symbolic, abstract, and rigorous cognitive features.
Natural mathematics and natural logic
MAGNANI, LORENZO
2014-01-01
Abstract
In his article “Why Proof? What is a Proof?” (2008) Carlo Cellucci focuses on so-called natural mathematics and natural logic, centering on mathematics and logic embodied in organisms as a result of natural selection, and stressing the different role of “artificial mathematics and logic”, that is, mathematics and logic as disciplines. I will provide further insight into this interplay. The first issue is related to the importance of increasing logical knowledge of abduction: Cellucci himself clearly shows how the study of abduction helps us to extend and modernize the classical and received idea of logic, understood merely as a corpus of axiomatic systems. The second refers to some ideas deriving from so-called distributed cognition and concerns the role of logical models as forms of cognitive externalizations of preexistent informal human reasoning performances. In this perspective, natural mathematics and logic are seen as constitutively intertwined with their “artificial” counterparts. Logical externalization in objective formal systems, communicable and sharable, is able to grant stable perspectives endowed with symbolic, abstract, and rigorous cognitive features.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
